Growth or decay

Question

Does the following function represent exponential growth or decay? What is the percent rate of change to the nearest tenth of a percent? 

y=(1.2)^-4x

Answer 1

The general form of an exponential is:

 

    y = a·b^x  where b = (1 + rate)

 

If b<1, it is decay.  If b>1, it is growth.  But since the exponent is negative, you have to be a bit careful.  Your equation is (a=1 in your equation):

 

     y = (1.2)^-4x = (1.2^-1)^4x = (1/1.2)^4x = (0.8333)^4x

 

So b is actually less than one and you have decay.  The rate can be determined from:

 

     b = 1 + rate

 

Plug in b = 0.833 and compute the rate in decimal.  Convert to %.